A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems

This paper concerns the problem of robust stabilization of autonomous and non-autonomous fractional-order chaotic systems with uncertain parameters and external noises. We propose a simple efficient fractional integral-type sliding surface with some desired stability properties. We use the fractional version of the Lyapunov theory to derive a robust sliding mode control law. The obtained control law is single input and guarantees the occurrence of the sliding motion in a given finite time. Furthermore, the proposed nonlinear control strategy is able to deal with a large class of uncertain autonomous and non-autonomous fractional-order complex systems. Also, Rigorous mathematical and analytical analyses are provided to prove the correctness and robustness of the introduced approach. At last, two illustrative examples are given to show the applicability and usefulness of the proposed fractional-order variable structure controller.